Emergent systems exhibit complex behavior arising from the interactions of many simple components. This talk will give an overview of three research projects in which the activities of many simple autonomous robots need to be coordinated so as to give desired high-level behavior. First, in a collective construction task inspired by termites, robots build structures according to user-specified designs. Next, in a collective locomotion task inspired by cellular slime molds, a robot comprising an unknown number of independent modules with unknown connectivity needs to achieve effective movement. Finally, performance considerations under severe constraints inform the design of micro aerial vehicles inspired by honeybees. The talk will highlight challenges and progress in these areas, and discuss general principles that can be used in other systems.